Hopcroft karp Algorithm implementation and tests (#6465)

* Add Hopcroft-Karp algorithm and tests * Adding wikipedia url for Algorithm * fixing test issues * remove unused field flagged by PMD
2025-12-19 07:00:35 +08:00 · 2025-08-14 20:42:51 +03:00
parent 57c6b033d1
commit 657f433413
2 changed files with 236 additions and 0 deletions
--- a/src/test/java/com/thealgorithms/graph/HopcroftKarpTest.java
+++ b/src/test/java/com/thealgorithms/graph/HopcroftKarpTest.java
@@ -0,0 +1,133 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for Hopcroft–Karp algorithm.
+ *
+ * @author ptzecher
+ */
+class HopcroftKarpTest {
+
+    private static List<List<Integer>> adj(int nLeft) {
+        List<List<Integer>> g = new ArrayList<>(nLeft);
+        for (int i = 0; i < nLeft; i++) { // braces required by Checkstyle
+            g.add(new ArrayList<>());
+        }
+        return g;
+    }
+
+    @Test
+    @DisplayName("Empty graph has matching 0")
+    void emptyGraph() {
+        List<List<Integer>> g = adj(3);
+        HopcroftKarp hk = new HopcroftKarp(3, 4, g);
+        assertEquals(0, hk.maxMatching());
+    }
+
+    @Test
+    @DisplayName("Single edge gives matching 1")
+    void singleEdge() {
+        List<List<Integer>> g = adj(1);
+        g.get(0).add(0);
+        HopcroftKarp hk = new HopcroftKarp(1, 1, g);
+        assertEquals(1, hk.maxMatching());
+
+        int[] leftMatch = hk.getLeftMatches();
+        int[] rightMatch = hk.getRightMatches();
+        assertEquals(0, leftMatch[0]);
+        assertEquals(0, rightMatch[0]);
+    }
+
+    @Test
+    @DisplayName("Disjoint edges match perfectly")
+    void disjointEdges() {
+        // L0-R0, L1-R1, L2-R2
+        List<List<Integer>> g = adj(3);
+        g.get(0).add(0);
+        g.get(1).add(1);
+        g.get(2).add(2);
+
+        HopcroftKarp hk = new HopcroftKarp(3, 3, g);
+        assertEquals(3, hk.maxMatching());
+
+        int[] leftMatch = hk.getLeftMatches();
+        int[] rightMatch = hk.getRightMatches();
+        for (int i = 0; i < 3; i++) {
+            assertEquals(i, leftMatch[i]);
+            assertEquals(i, rightMatch[i]);
+        }
+    }
+
+    @Test
+    @DisplayName("Complete bipartite K(3,4) matches min(3,4)=3")
+    void completeK34() {
+        int nLeft = 3;
+        int nRight = 4; // split declarations
+        List<List<Integer>> g = adj(nLeft);
+        for (int u = 0; u < nLeft; u++) {
+            g.get(u).addAll(Arrays.asList(0, 1, 2, 3));
+        }
+        HopcroftKarp hk = new HopcroftKarp(nLeft, nRight, g);
+        assertEquals(3, hk.maxMatching());
+
+        // sanity: no two left vertices share the same matched right vertex
+        int[] leftMatch = hk.getLeftMatches();
+        boolean[] used = new boolean[nRight];
+        for (int u = 0; u < nLeft; u++) {
+            int v = leftMatch[u];
+            if (v != -1) {
+                assertFalse(used[v]);
+                used[v] = true;
+            }
+        }
+    }
+
+    @Test
+    @DisplayName("Rectangular, sparse graph")
+    void rectangularSparse() {
+        // Left: 5, Right: 2
+        // edges: L0-R0, L1-R1, L2-R0, L3-R1  (max matching = 2)
+        List<List<Integer>> g = adj(5);
+        g.get(0).add(0);
+        g.get(1).add(1);
+        g.get(2).add(0);
+        g.get(3).add(1);
+        // L4 isolated
+
+        HopcroftKarp hk = new HopcroftKarp(5, 2, g);
+        assertEquals(2, hk.maxMatching());
+
+        int[] leftMatch = hk.getLeftMatches();
+        int[] rightMatch = hk.getRightMatches();
+
+        // Check consistency: if leftMatch[u]=v then rightMatch[v]=u
+        for (int u = 0; u < 5; u++) {
+            int v = leftMatch[u];
+            if (v != -1) {
+                assertEquals(u, rightMatch[v]);
+            }
+        }
+    }
+
+    @Test
+    @DisplayName("Layering advantage case (short augmenting paths)")
+    void layeringAdvantage() {
+        // Left 4, Right 4
+        List<List<Integer>> g = adj(4);
+        g.get(0).addAll(Arrays.asList(0, 1));
+        g.get(1).addAll(Arrays.asList(1, 2));
+        g.get(2).addAll(Arrays.asList(2, 3));
+        g.get(3).addAll(Arrays.asList(0, 3));
+
+        HopcroftKarp hk = new HopcroftKarp(4, 4, g);
+        assertEquals(4, hk.maxMatching()); // perfect matching exists
+    }
+}